From: ISMB-96 Proceedings. Copyright © 1996, AAAI (www.aaai.org). All rights reserved.
A Knowledge-Based
Method
for Protein
Prediction
Structure
Refinement
and
t t, David K. Tchengt and James M. Fenton
Shankar SubrnmaniAm
tBeckmanInstitute, National Center for SupercomputingApplications,
*#Center for Biophysics and Computational Biology &
Department of Molecular and Integrative Physiology,
University of Illinois at Urbana-Champaign,Urbana, IL 61801
Abstract
The native conformation of a protein, in
a given environment,
is determined
entirely
by the various interatomic
interactions
dictated by the amino acid
sequence (1-3).
We describe
here
knowledge-based approach for protein
structure
assessment and prediction.
Using a well-defined
set of highresolution protein structures,
we have
derived statistical potentials, in the form
of atom-pairwise distance probability
density
functions.
These provide a
description
of pairwise interatomic
interactions
of native proteins.
When
applied to highly randomized and noisy
structures of proteins distinct from the
basis set, native-like
structures were
obtained to very high precision (_<2/k).
The examples tested include proteins of
all sizes (from 38 up to 461 amino acids
long) and diverse topological structures
(alpha, beta and alpha-beta classes). The
potentials appear to be sensitive enough
to recognize subtle distortions
from a
native
packing
structure
and in
optimization
of structures
drive them
consistently
to a higher probability.
Therefore they provide a powerful tool
for refinement of X-ray and NMRderived
structures at arbitrary degrees of initial
precision.
Efforts to fold a protein from a random
structure corresponding to its sequence have
met with little success. The objective of a
number of these efforts has been to minimize
an energy or free energy function that
describes interatomic interactions (4-6)
obtain the folded protein structure. These
218 ISMB-96
energy functions have been obtained from
theoretical
or phenomenological
considerations. The direct energy function
methods include use of mechanics force-fields
(7) and semi-empirical force fields (8,9).
traditional molecular mechanics force fields
use energy functions for bonds, angles,
torsions
and for pairwise
nonbonded
interactions.
These have been employed for
both local structure
predictions
and in
conjunction with crystallographic
data or
distance-constraints
obtained from magnetic
resonance methods (10,11).
Knowledgederived potential functions have also been
employed to fold protein sequences into
structures to a limited degree of success.
These include residue-based profiles (12,13),
lattice models (14-16), threading methods(1720) and homologymodels (21,22).
Knowledge-Based Potentials
The problem of describing a folded protein in
terms of the optimal interatemic interactions
can be inverted to obtain energy functions that
are optimal for folded protein structures. A
majority of these methods use high resolution
protein structures to derive pairwise residuelevel contact information or in a few cases
atom level interactions
(23,24).
The
knowledge of pairwise atomic contacts in
knownprotein structures reflects the relative
probability of finding atom pairs at specified
distances and hence can provide a measure of
the free energy of interaction. The theoretical
foundations for this stem from the Boltzmann
principle, whichasserts that the probability of
a given atomic configuration for a protein
structure is related to the free energy.
Minimizing the free energy of a protein is
equivalent to maximizing concomitantly all
the pairwise atomic distance probabilities. We
note here that this is strictly true if and only if
the probabilities are truly independent.
Wehave used the above principle to develop
statistically-derived
potentials for refining
and predicting protein structures. Wederive
the statistical potentials as probability density
functions (PDFs)that describe the distribution
of distances between different
groups of
atoms. Each heavy atom in an amino acid is
described as a group and the twenty amino
acids yield 167 groups of atoms. The distance
data for constructing the distributions
is
obtained from a database of 380 unique
protein structures.
The latter
set is
constructed from a larger database of protein
structures by requiring each memberof the
unique set to have a resolution of less than 2.5
A and any two members to have less than 50
percent sequence homology as defined by
standard BLASTprotocols (25). Distance
examples are generated from this database for
every pair of atomic contacts and these are
used to construct the PDFs. The conditional
pairwise distance PDFs take the form of
Probability (XI Ri,Ak,Rj,~I,Sn), where, X is
the distance, Ri and Rj represent residue
indices, Ak and A1 atom indices, and Sn
represents the sequential distance between
theresidues
Ri andRj.Thetotalprobability
of pairwise
distance
contacts
in a protein
is
given by combining the conditional
probabilities,
P(protein)
= I-I P(XIRi, AK,Rj,A1,S,)
k.l.i.j.S,
where the indices run over all atoms, residues
and the specified sequential distances. The
sequential distance is used so as to preserve
the sequentially contiguous interactions that
give rise to secondary structure in proteins.
The case where n=0 represents the intraresidue PDFs which are a measure of the
configurational and conformational geometry
of the amino acid considered. Weobserve that
for PDFs of atom pairs separated by more
than 3 residues there are no specific secondary
structure interactions and we consider these
as tertiary PDFs.
A unique PDF is formed for each unique
combination
of Ri, Rj, Ak, Al and Sn. For
instance,
P(XI VaI,CGI,Leu,CD1,3)
represents
the PDFfor Val CG1-LeuCD1 atompairsfor
whichthe parentresidues
Val and Leu are
sequentially
in 1-3positions.
A keyproblem
in deriving
these
potentials
is thenon-uniform
distribution
of pairwisedistances
in the
distance
space.To overcome
thislimitation
statistically
rigorousmethodsof kernel
densityestimation
and maximumlikelihood
evaluation
are used to construct
the PDFs
(26).
Methods
The January 1994 relase from the Brookhaven
Protein Data Bank (3611 protein chain
sequences) was used in building the nonhomologous set of proteins.
Each entire
sequence was compared against all of the
sequences in the database. Sets of homologous
protein chains were created with each set
containing proteins which had more than 50%
identity.
Amongst the homologous set, the
highest resolution protein was chosen as a
representative [28]. Thus a list of unique
chains was selected.
The total number of atom types corresponding
to the heavy atoms in the twenty amino acids
is 167. The pairwise atomic distance PDFs
are generated for intra residue, residues
related by positions, n-n+l, n-n+2 and n-n+3
and each of the other pairs, within 10/~ form
the tertiary PDFs. The n-n+1, n-n+2 and nn+3 and tertiary
PDFS are computed
seperately for N to C and C to N terminal
directions.
The PDFs are assumed
independent
of each other.
The only
additional PDFused is one corresponding to
the S-S bond in disulfides. The total number
of PDFsthus amount to 112,226 types and the
number of atomic distance pairs in the 380
proteins considered are 80,670,588. The
compressed PDFs occupy approximately 115
MBytes of storage. The computational time
required for constructing all the PDFsis 268
hours on a single R8000 SGI processor. The
annealing of medium sized protein from a
random structure takes about 40 hours on a
single R8000processor.
Subramaniam
219
Kernel Density Estimation (KDE) coupled
with Bias Optimization (BO) used to construct
the distance PDFs. KDEalgorithm employs a
normal distribution for the "kernel" function.
The algorithm first distributes the distance
examples along the distance axis, and then
slides the kernal function accross the distance
axis while computing a weighted sum. The
result of this convolution is then normalized so
the area under the curve sums to 1.0. The
final result is a PDF that estimates the
probability of any pairwise distance. The
height of the curve is proportional to the
probability. In other words, a distance D1 is
roughly twice as likely as distance D2 because
the Drs probability P1 is twice as large as
D2’s probability P2.
The width of the kernel, sigma, is a critical
parameter for obtaining optimal PDFs. If
sigmais too small, the result will be a "jagged"
distribution
that "overfits"
the data.
Conversely, if the sigma is too large,
important local changes in probability will be
smoothedover which will "underfit" the data.
The solution is to optimize the choice of sigma
by selecting a range of different sigmas and to
select the sigma that performs the best.
The precise definition of the performance(i.e.,
the objective function for optimization) is
important. Weneed a measure that reflects
the predicted performance of the system when
operating on new (i.e., unseen) problems.
our method we measure performance by
repeatedly selecting a random subset (e.g.,
90%)of all examplesfor training (i.e., inducing
the PDFs) and using the rest of the examples
for testing (i.e., predicting distances). The
process is repeated a number of times and the
accuracy of predictions is averaged over all
trials.
The accuracy of a prediction
is
measured in terms of maximumlikelihood
principle (MLP). The MLPstates that the
best probability distribution function is the
one that makes the joint probability of the
examples most likely.
i=t
performance= l-I P(Di)
i=l
22O ISMB-96
For numerical considerations, this equation is
expressed in terms of logs and is of the form:
i=t
log(performance)Y.logP(Di
i=l
We form the PDFs using only the training
examples and test the performance only on the
test examples. In summary the choice of a
sigma is dependent on the average likelihood
of test examples when evaluated against PDFs
formed from the training examples across
multiple partitions of the training and testing
set.
Further, squared distance division is carried
out to obtain radial density normalization. In
Fig. 1, we present exemplar PDFs for 4
categories.
The height of the resulting
normalized PDF curve is a measure of the
relative probability of finding two atoms
belonging to two residues at the defined
distance. Wenote that all but the tertiary
probabilities
when normalized by squared
distance go to zero before 10/k
and the
tertiary probabilities reach a plateau value by
10/~. We compute a mean probability from
these truncated PDFcurves. In evaluations of
protein structures, we subtract the expected
meanprobability value corresponding to each
PDFfrom the actual probability to assess how
significantly better or worse that specific pair
interaction is as comparedto an average pair
interaction of that type. Further, we can
obtain either atomic or residue profiles of a
protein, based on averaging over interactions
of each atom or over each residue respectively
and these profiles provide a relative measure
of deviation from ideality of the interactions of
the defined atom or residue in the context of
the protein structure.
The total normalized probability summedover
all pairwise atomic probabilities
was
computed for all the 380 proteins data set
chosen for PDFconstruction.
It was found
that there was a correlation between the total
logarithmic probability and the resolution of
the structures.
The Spearman rank
correlation for normalized probabilities
yielded a Z-value of-5.6 and a P-value less
than 0.0001.
In the annealing
procedure,
atoms are
incrementally
moved in the direction
which
maximizes probability
of all the atom’s
interactions,
weighting each interaction
equally. In each stop, atoms are moved one at
a time and the order in which each atom is
moved is randomized each step. An atom is
moved by defining a sphere of radius 0.2 A
around it,
and randomly selecting
100
candidate points within the sphere using a
uniform sampling distribution.
The candidate
points are evaluated one at a time and the
difference
between the candidate
atom
probability
and current atom probability
is
calculated.
The standard
probabilistic
simulated annealing acceptance criterion
is
used to determine when to move the atom.
Table 1. Comparison of Total Probabilities
The only additional
constraint
used in
addition to the distance PDFs was a torsional
term that was biased towards the correct
chirality
for each amino acid. For all the
optimization
experiments,
200 stops of the
annealing
procedure
was employed.
The
control parameters for annealing, the tertiary
interactions
weight, the chirality weight, and
the temperature used for simulated annealing
changed each step based on linear schedules.
The weight of tertiary interactions was varied
from 0.0 to 1.0, the weight of the chirality
term varied
from 0.08 to 0.01, and the
temperature in normalized probability
units
varied from 1/32 to 1/1000.
of Low and High Resolution Protein
Pairs
Protein
PDB Name
(Resolution
in .~)
Total
distance
log(prob)
PDB Name
(Resolution
in/~)
^Total
distance
log(prob)
Pancreatic Trypsin Inhibitor
Alpha Bungaroto~rin
Cytochrome B5
Plastocyanin
Parvalbumln
Cytochrome B562
Pseudoazurin
Proteinase A
Dihydrofolate
Reductase
Lysozyme
Alpha-Lytic Protease
Actinidin
Acid Proteinaso
Thermolysin
Glutathione Reductase
3pti(1.50)
2ebx(1.40)
2b5c(2.00)
lpcy(1.60)
lcpv(1.85)
156b(2.50)
laza(2.00)
lsga(2.80)
ldfr(2.50)
llzm(2.40)
lalp(2.80)
lact(2.80)
lapr(2.~0)
ltln(2.30)
2grs(2.00)
-0.0043
-0.0230
0.0215
-0.0113
-0.0052
-0.0165
-0.0324
-0.0472
-0.1858
-0.0142
-0.0510
-0.2524
-0.1147
-0.8905
-0.1496
9pti(1.22)
3ebx(1.40)
365c(1.50)
lplc(1.33)
4cpv(1.50)
256b(1.40)
2aza(1.80)
2sga(1.50)
3dfr(1.70)
31zm(1.70)
2alp(1.70)
2act(1.70)
2apr(1.80)
3tin(1.60)
3grs(1.54)
-0.0037
-0.0178
0.0338
-0.0082
0.0361
0.0877
-0.0230
-0.0141
-0.1221
0.0421
-0.0192
-0.0045
-0.0064
0.0082
0.0016
^ The total
PDF Profiles
distance
log (probability)
of Protein
is both meanvalue and r-squared normalized.
Structures
The PDF curves represent local structure and
packing interactions
in proteins.
An ideal
protein would have every pair of atoms in the
regions of high or highest probability and thus
possess optimal interactions.
In general
higher resolution
protein structures
have
higher pairwise atomic probabilities.
In Table
1, we compare the total
logarithmic
probability
scores averaged over all the
pairwise interactions
in the protein for 15
protein pairs,
whose structures
have been
obtained at two resolutions.
These proteins
were not included in the 380 unique protein
set used to construct the PDFs. In each case
the higher resolution protein structure has a
higher probability
score. In one case, where
the structures
had the same resolution,
the
one with a lower crystallographic
R-factor had
Subramaniam
221
’
o’..-. 10.0L
(~
tO
E 8.0
’~-
’
’
-
~
,,
/
I I
~ l
6.0
,o
’
’
{~
~I
/
\
~
J
Val CG1- Leu CD1
--N N+I
’
N, N+2
--- N, N+3
"
J
\
¯ J 2.0
%
"- 0.0
0.0
~
~’ ~’~---’------"-------"-10.0
15.0
5.0
Distance in A
Figure 1. Representative PDFsfor Val CG1-LeuCD1atom pairs. N, N+I represents adjacent
VaI-Leu residues. N,N+2 those seperated by one residue, N,N+3 those seperated by two
and > N, N+3 stands for all other Val CG1-LeuCDlatompairs. The PDFsare first normalized to
unity and then by radial density.
"O
N
-
EO
n
o._1
;. ..........
_n.an
’,~,~,,
0
I
11zm
,
[
50
,
,
100
’
150
RESIDUE NUMBER
Figure 2.. Comparisonof (A) three dimensional structures of T4 phagelysozyme at 2.4 (1LZM)
and 1.7 A (3LZM) resolution, The darker and light shades represent low and high distance
probability pairwise atomic contacts. (B) Residue profiles of 3LZMand 1LZM.The positive
log(Probability) values indicate better pairwise atomic contacts averaged over all atoms for the
residue. The C-terminal domain of 3LZMis better refined than that of 1LZM.
222
ISMB-96
the protein although the overall topology of
the two structures was similar. Despite the
low molecular mechanics energies of both
structures
one of them was flawed by the
phase shift. In Fig. 3, we compare the total
and individual PDFresidue profiles of the two
structures. The overall residue profiles show
clearly that the structure 2GN5is not nativelike owing to the large numberof low distance
probabilities.
Analysis of the individual
profiles reveals that the intra-residue and
neighbour residue profiles obtained from
pairwise interatomic interactions show that
the PDF method is able to discriminate the
non native-like local geometryof the residues.
The structure 0GVPis consistent with native
protein structures.
a higher probability
score. To further
illustrate the regions in the protein that have
more ideal interactions as defined by the PDF
scores, we show a comparison of the two
structures and the residue-wise probability
profiles of T4 phage lysozyme, 31zm at 1.7 A
resolution and llzm at 2.4 A resolution, in Fig.
2. The C-terminal domain is better resolved
in 31zmas reflected by the higher probability
scores.
The x-ray structure of the single strand DNAbinding Gene V protein was solved by two
groups of researchers and both used the x-ray
data in conjunction with molecular mechanics
methods to refine the structures (2GN5 and
0GVP). One of the structures (2GN5) had
phase shift error in the N-terminal domain of
1.0
oGvP
<
o
-1.0
r~
rl
o -2.0
o
-3.0
2GNS
B.
A.
,
0
[
20
~
I
I
I
40
60
RESIDUENUMBER
80
Figure3. (A) Comparison
of the three dimensional
structuresof the single-strandDNAbinding
GeneV protein (2GN5
and0GVP).(B). Comparison
of the residueprofiles of the twostructures.
................................
Threading of a Sequence into Structural
Motifs
In order to examine the value of PDFs in
assessing structural fragments of naturally
occuring proteins, we examined a structured
fragment from the peptide GCN[28]. The
structure of the native fragment is helix-like.
Wethreaded the sequence into well-defined
secondary-structural
motifs extracted from
high-resolution
structures
and energyminimized the structures
using molecular
mechanics methods. The various structural
motifs into which the sequence was threaded
were analyzed for PDF profiles.
Fig 4
presents
the structural
motifs and a
comparison of the PDFprofiles. Despite the
very low molecular mechanics energies of the
turn-like fragments, the PDFresidue profiles
show the highest probability for the native
structure.
Annealing Noisy Protein Structures
An important use of the knowledge-based
potentials is in the refinement of a non-native
or poorly resolved protein structure to a native
state. In conventional methods, optimization
on an energy landscape is carried out to obtain
the native protein structure. The potential
functions that yield the energy landscape are
based on either molecular mechanics-based, x-
Subramaniam 223
ray structure
factors,
NOE distance
constraints
or combinations of these (27).
Molecular mechanics functions yield a very
rough energy landscape and the resulting
multiple minima render energy optimization
complex.
By virtue
of being extremely
specific,
our statistical
potentials,
which
describe each pairwise atomic interaction
in
accurate detail, yield a smooth and arguably
unique minimum in the energy landscape and
hence are ideally suited for folding non-native
and noisy into
native
structures.
We
demonstrate
the power of this method for
diverse classes of proteins and suggest its
possible
use with low resolution
x-ray or
partial NOEdata.
We use an annealing procedure to predict the
structures of the proteins listed in Table 2,
starting
from noisy structures.
Each of the
initial structures was created by adding noise
to the x-ray structure.
Noise was added by
defining a sphere with a 10/~ radius around
each atom and randomly relocating
the atom
within the sphere using a uniform sampling
distribution, i.e., all points within the sphere
were treated as equally likely.
Table 2. RMSDeviation and Total Probabilities
comparison of the x-ray structure.
Protein
Pancreatic Trypsin
lnhlbitor(9pti)
Alpha Bungarotoxin (3ebx)
Cytochrome B5 (3b5c)
Plastocyanin (lplc)
Parvalbnmln (4cpv)
Cytochrome B562 (256b)
Pseudoazurin (2aza)
Proteinase A (2sga)
Dihydrofolate Reductase (3dfr)
Lysozyme (31zm)
Alpha-Lytic Protease (2alp)
Actinidin (2act)
Acid Proteinase (2apr)
Thermolysin (3tin)
Glutathione Reductase (3grs)
^ The total
224
ISMB-96
Table 2 shows the r.m.s, deviations of the 15
proteins
annealed
from a randomized
structure as compared to the x-ray structures.
These proteins
are chosen so as represent
diversity
in size, packing and fold and are
excluded from the set from which PDFs are
constructed. In all of the examples studied, a
well-connected compact topological structure
was formed in the early stages of annealing,
i.e., within 50 steps of optimization and the
resulting structures are similar to the x-ray
structures.
A large contribution to the small
RMSdeviations
from the x-ray structures
stem from the solvent exposed side-chain
orientations.
The PDFs do not take into
account explicitly
the protein-solvent
interactions
or crystal contacts.
However,
they improve the interactions
in the protein
interior so as to optimize packing. Wewish to
note, that optimization
using covalent
constraints
alone yielded structures
which
were sequentially
connected but lacking both
secondary structures
and tertiary
packing
arrangements.
of Refined Proteins.
Number of All
Residues
Atom(Number
RMSD
of Atoms) in/~
(random)
58 (453)
7.826
62 (474)
85 (692)
99 (737)
108 (806)
106 (825)
129 (975)
181 (1258)
162 (1293)
164 (1308)
198 (1390)
218 (1645)
325 (2402)
316 (2431)
461 (3498)
distance log (probability)
7.849
7.810
7.803
7.791
7.782
7.784
7.751
7.743
7.741
7.738
7.754
7.787
7.784
7.777
All AtomRMSD
in/~
(refined)
The RMSDsrefer to
1.998
Back
-bone
AtomRMSD
in/~
1.557
2.040
2.085
2.024
2.180
1.913
2.128
2.129
1.930
2.081
2.144
2.312
2.142
2.051
2.157
1.496
1.696
1.633
1.636
1.475
1.558
1.657
1.517
1.610
1.618
1.801
1.687
1.655
1.652
^Total dist.
log(prob)
is both meanvalue and r-squared normalized.
-0.026
-0.042
-0.001
-0.030
0.001
0.036
-0.028
-0.041
-0.017
0.006
-0.040
-0.038
-0.027
-0.014
-0.016
AI
Native
Nphahelix
Polyprolinehelix
~.,&
BetaI turn
OB~II turn
<~- --~Type VI turn
O"
4~’ Tyoe
VIII turn
-0.40
TypeVI turn
BetaII turn
\\
\\""t
17
TypeVIII turn
;/
#11
~’’~t
15
¯
’
19
RESIDUE NUMBER
’
21
Figure 4. (A) The structural motifs into which the GCNpeptide fragment is threaded.
Thestructural motifs include native, standardalpha helix, poly proline helix, beta strand,
beta I turn. beta II turn, type VI turn andTypeVIII turn. (B) Theresidueprofiles of the
peptide in the abovestructural motifs are compared.The native structure has the highest
overallprofile.
Subramaniam 225
X-Ray
Randomized
Optimized
Optimized
Native
m- ~~< 0.0
m -1.0
O
i’T
n -2.0
-3.0
i l
[
0
",
3dfr X-ray structure
I
.... 3dfr Optimized
50
100
150
RESIDUE NUMBER
Figure 5. (A) Comparison
of the randomized,annealedandx-ray structure of the 461
residue glutathione reductase(3grs), Only Caatomsare displayed. (B) Comparison
of the annealedandx-ray structuresof the 162-residuedihydrofolatereductase(3dfr).
Theatomsare color codedsuch that the darker shadeindicates lower pairwise atom
distanceprobabilities. Thex-ray structure has numerous
improbablecontacts(darker
lines), whichare correctedin the annealed
structure(lighter lines). (C) Residue-wise
probabilityprofiles for the x-ray andrefineddfr structures.
226
ISMB-96
X-Ray
Predicted
Figure 6. Comparisonof the x-ray and annealedstructures of cytochromeB562(256b).
Helices are representedby cylinders and the side chains thatrepack in PDF-based
annealing
are represented by spheres. The x-ray structure showsthe hemegroup and the packing of
the side chains and the annealedstructure showsthe packing reorganization; the hemegroup
wasnot consideredin the PDF-based
annealing.
Randomized
40 Steps
10 Steps
50 Steps
20 Steps
200 Steps
30 Steps
X-Ray
7. Structures of T4 phagelysozymeat different stages of annealingare shown.Thecolor
codingis darker (low) to lighter (high probabilities). Therandomized
structure anneals
compactstructure in the early stagesand to secondarystructures in the first 50 steps. The
structure after 200 steps of annealinghas achievedmost of the secondarystructure in the
actual protein andhasprobabilities close to thosein the x-ray structure.
Subramaniam
227
In Fig. 5, we present the initial
noisy,
annealed and the x-ray structures of the two
proteins, 461-residue glutathione reductase
(3grs) and 162-residue dihydrofolate reductase
(3dfr). In the latter, we also compareresidueaveraged PDFprofiles of the refined and the
native x-ray structures. The x-ray structure
has numerous improbable contacts, which are
refined in the annealed structure.
In Fig. 6, we present the annealed and the xray structures of the protein cytochromeB562,
(256b). Wechoose this protein to test the PDF
potentials in assessing proteins that contain
prosthetic groups. In the cytochrome B562,
the non-inclusion of the prosthetic hemegroup
in the PDF optimization does not appear to
affect the overall structure. Fig. 4 shows that
the side chain atoms of residues in contact
with the heme, Met 7, Ash 11, Phe 65, Arg 98
and Arg 106, reorient to provide better
packing in the optimized structure which does
not contain the heme group. Helices 3 and 4
in the native protein movetowards each other
so as to yield better packing. Despite the
deviations in the local region near the
prosthetic group, the rest of the protein is
annealed to the native structure.
We examined the annealing of the protein
structures with the PDFmethod, by following
the folding process in bacteriophage T4
lysozyme. In Fig. 7, we present different
stages of annealing of a noisy structure, with
the colors representing the transition of the
structure
from low probability
and
consequently high energy to high probability
interactions.
The early stages of annealing
produces compactness, while the secondary
structures are formed within circa 50 steps.
At 200 steps of annealing the protein has
optimized close to the actual structure. The
folding process showsthe specificity and hence
the accuracy of these statistical potentials for
native protein structure.
In summary, we have developed statistical
potentials that describe the folded state of
proteins accurately. These potentials are
independent of protein sequence homologies,
secondary structures or folds and contain
information at the fundamental level of
pairwise atomic interactions specific for each
228 ISMB-96
pair of residues.
The distance-based
statistical
potentials appear to be ideally
suited for combining with x-ray and NMR
structural refinement methods.
Acknowledgements
We thank Drs. E. Jakobsson, S. Sligar, A.
Crofts
and C. Wraight for valuable
discussions.
We acknowledge a metacenter
computer allocation and computer resources at
the National Center for Supercomputing
Applications.
References
1. Anfinsen, C.B. Principles that govern the
folding of protein chains. Science 18 ], 223230 (1973).
2. Dill, K.A. Dominant forces in protein
folding. Biochemistry 29, 7133-7155(1990).
3. Lattman, E.E. and Rose, G.D. Protein
folding - What is the question? Proc. Natl.
Acad. Sci. U.S.A. 90, 439-441 (1993).
4. Levitt, M. and Warshel. A. Computer
simulation of protein folding. Nature 253,
694-698 (1975).
5. Godzik, A., Kolinski, A. and Skolnick, J.
Are proteins ideal mixtures of amino acids Analysis of energy parameter sets. Protein
Science 10, 2107-2117 (1995).
6. Elofsson, A., Le Grand, S.M., Eisenberg, D.
Local moves - An efficient
algorithm for
simulation of protein folding. Proteins: Struct.
Funct. Genet. 23, 73-82 (1995).
7. McCammon, J.A. and Harvey,
Dynamics of Proteins and Nucleic
(Cambridge: Cambridge University
1987).
S.C.,
Acids.
Press,
8. Ponder, J.W. and Richards, F.M. Tertiary
templates for proteins - Useof packing criteria
in the enumeration of allowed sequences for
different structural classes. J. Mol. Biol. 193,
775-791 (1987).
9. Srinivasan, R. and Rose, G.D. LINUS: A
hierarchic procedure to predict the fold of a
protein. Proteins: Struct. Funct. Genet. 22, 8199 (1995).
10. Brunger, A.T., Kuriyan, J. and Karplus,
M. Crystallographic R-factor refinement by
molecular dynamics. Science 235, 458-460
(1987).
11. Branden, C.I. and Jones, T.A. Between
objectivity and subjectivity. Nature 343, 687689 (1990).
12. Crippen, G.M. Prediction of protein
folding from amino acid sequence over discrete
conformation spaces. Biochemistry 30, 42324237 (1991).
13. Luthy, R., Bowie, J.U. and Eisenberg, D.
Assessment of protein models with threedimensional profiles.
Nature 356, 83-85
(1992).
14. Sali, A., Shakhnovich, E. and Karplus, M.
Howdoes protein fold? Nature 369, 248-251
(1994).
15. Dill, I~A., Bromberg,S., Yue, K., Fiebig,
K.M., Yee, D.P., Thomas, P.D. and Chan, H.S.
Principles of protein folding - A perspective
from simple exact models. Protein Sci. 4, 561602 (1995).
16. Karplus, M. and Sali, A. Theoretical
studies of protein folding and unfolding. Curr.
Opin. Struct. Biol. 5, 58-73 (1995).
17. Sippl, M.J. and Weitckus, S. Detection of
native-like models for amino acid sequences of
unknown three-dimensional
structure in a
data base of known protein conformations.
Proteins: Struct. Funct. Genet. 13, 258-271
(1992).
18. Jones, D.T., Taylor, W.R. and Thornton,
J.M. A new approach to protein
fold
recognition. Nature 358, 86-89 (1992).
19. Holm, L. and Sander, C. Protein
structure comparison by alignment of distance
matrices. J. Mol. Biol. 233, 123-138 (1993).
20. Bryant, S.H. and Lawrence, C.E. An
empirical energy function for threading
protein sequence through the folding motif.
Proteins: Struct. Funct. Genet. 16, 92-112
(1993).
21. Hearst, D.P. and Cohen, F.E. GRAFTER
A computational aid for the design of novel
proteins. Prot. Eng. 7, 1411-1421(1994).
22. Sali, A. and Blundell, T.L. Comparative
protein modeling by satisfaction of spatial
restraints. J. Mol. Biol. 234, 779-815 (1993).
23. Sippl, M.J. Calculation of conformational
ensembles from potentials of mean force. An
approach to the knowledge-basedprediction of
local structures in globular proteins. J. Mol.
Biol. 213, 859-883 (1990).
24. Sun, S. Reduced representation model of
protein structure prediction: Statistical
potential and genetic algorithms. Protein Sci.
2,762-785 (1993).
25. Altschul, S.F., Gish, W., Miller, W.,
Myers, E.W. and Lipman, D.J.J. Mol. Biol.
215, 403-410 (1990).
26. Hogg, R.V. and Tanis, E.A. Probability
and Statistical
Inference
(New York:
MacMillan Publ. Company, 1988).
27. Brunger,
A. T. and Nilges,
M.
Computational challenges for macromolecular
structure
determination
by x-ray
crystallography
and solution
NMRspectroscopy. Q. Rev. Biophys. 26, 49-125
(1993).
28. Walsh, L.L. An annotated guide to the
Brookhaven Protein Databank, classification
and comparisons of protein structures.
(Doctoral Dissertation
Submitted to the
University of Illinois, 1994).
29. The color-coded versions of figures in the
manuscript can be found on the WWW,
whose
URLis
http’J/bioweb.ncsa.uiuc.edu/doc/ISMB96.html.
Subramaniam
229